Measurement of the chemical composition of ancient coins with portable XRF

1. Introduction

1.1. Methods for elemental analysis of historical artifacts

In archaeology many different characteristics of an artifact are of interest. One of these characteristics is the elemental composition of artifacts, which is the concentration of the chemical elements within the artifact. Knowledge of element composition can help assign the sample to a specific era or provide information about the provenience, production methods, or raw materials use^[1]. In general, such an elemental analysis might be performed with destructive, semi‑destructive and non‑destructive methods. Using destructive analytical methods, a sample is consumed during the measurement process. However, the size of the sample may be very small, so that only minor damage needs to be inflicted on the artifact. Central concepts for the comparison of different analytical methods are accuracy and precision of measurements are of great interest (see figure 1).

Some analytical methods deliver both precise and accurate data, some are only yielding either precise or accurate data, and some methods are limited in both precision and accuracy. Destructive methods like inductively coupled plasma mass spectrometry (ICP-MS)^[2] or inductively coupled plasma optical emission spectroscopy (ICP‑OES)^[3] can very precisely determine the elemental composition of the sample, based on sample sizes in mg or even in the sub-mg range^[4]. With a suitable calibration, these measurements will also provide high accuracy. With a laser coupled to the spectrometer, laser-ablation inductively coupled plasma mass spectrometry (LA-ICP-MS)^[5], samples can e.g. be taken from a small spot of a historical artifact with a diameter of less than 0.1 mm and only a few µm deep. In this sense, LA‑ICP‑MS might be called ›semi‑destructive‹ as such a spot is barely visible to the naked eye on a bigger artifact. Nevertheless, the artifact is not unharmed in a strict sense, so curators might remain skeptical of such a method. LA-ICP-MS needs no chemical sample treatment and therefore consecutive measurements can be made in short time, but its use remains limited due to the fact than an LA-ICP-MS is not a portable instrument. Artifacts that are to be measured must be brought in a scientific lab and despite its virtual non‑destructiveness, decisions of collection curators are needed to prevent or mitigate unnecessary influence on the artifacts. Although environments do exist, that foster such close relationships between humanities and scientists as the CRNS lab collaborating with the Louvre museum^[6], this is rather an exemption. On the other hand, there is a broad range of spectroscopic techniques that are in general non-destructive, e.g. nuclear magnetic resonance (NMR)^[7], infrared spectroscopy (IR)^[8], as well as X-ray fluorescence (XRF)^[9], that are all radiation based and have been successfully applied to historical artifacts. All these methods can be highly precise and have the potential for high accuracy, if calibrated. Also, Neutron activation analysis (NAA)^[10] can be classified as a non‑destructive method. Although NAA might lead to an activation of the sample during the investigation (i.e. the generation of a small amount of temporary or permanent radioactivity), the method has been used successfully multiple times^[11]. One advantage of NAA is that it can be calibrated relatively easily because matrix effects in the calibration are mostly negligible. Of the different spectroscopic methods, XRF is to be highlighted: XRF can deliver the elemental composition of a sample in a non-destructive way, there is a broad experience analysis of artifacts with different X-ray sources^[12] and second, small portable XRF spectrometers that can be used within the museum context are available for several years^[13]. In these devices, a small X-ray tube is used to irradiate the sample, and the equipment is small and light enough to place it on a simple tripod in any orientation. Hence it can be applied as well as to artifacts of any size or paintings without even moving them out of an exhibition environment. However, especially portable XRF is limited in both accuracy and precision, because both might be influenced by the sample geometry (e.g. surface structure and roughness). Generally, X‑ray fluorescence might also be induced using a particle beam (PIXE, for particle induced X‑ray‑emission)^[14] or the strong radiation of a synchrotron source^[15]: Both methods can be advantageous under different circumstances but are not portable.

However, the limitations of XRF that might hamper widespread use are:

1. XRF works better with heavier chemical elements, i.e. it is not well-suited for the analysis of the main components of organic materials,
2. possible matrix effects influence the accuracy of the results, i.e. the accuracy might decrease, especially if the object contains multiple chemical elements,
3. measurement results, especially precision, might be influenced by the sample surface geometry, as will be explained in more detail below,
4. XRF is generally not a high accuracy method, also depending on the sample composition,
5. measuring depth and width are limited, giving inconclusive results in the case of inhomogeneous materials.

With this work we want to show that XRF can be successfully applied when:

1. light chemical elements play no role (like in metal alloys),
2. matrix effects can be minimized using suitable calibration methods,
3. the influence of sample geometry can be estimated by a model,
4. high accuracy is not decisive e.g. for analyzing groups of artifacts, i.e. when several subsets of samples are compared to each other,
5. when enough measurement points are used, yielding a representative (and thus more precise) composition for a single object and allowing for a statistical approach when several samples are measured.

We will demonstrate this throughout this paper on the example of ancient Alexandrian coins from the Roman period, lead-bronze coins (drachms) and billon coins (tetradrachms) of Claudius (41–54 AD) and Nero (54–68 AD). We will explicitly show how some of the limitations of XRF can be overcome when measurements on a larger group of coins (n = 20) are performed and analyzed, revealing new information. We will show that accuracy as well as precision can be improved by making use of correction factors and a large number of single measurements for each coin. While this does not overcome completely the limitations of portable XRF, with these procedures data gained from large sample sets (e.g. of coins) might discover yet unknown trends and provide new insights.

1.2. Aim of this work

In this work, we describe how the influence of self-absorption on XRF-spectra can be corrected by introducing a correction factor (improving mostly accuracy) and how the influence of patina and surface effects can be minimized with multiple measurements (improving precision). Self-absorption correction factors were obtained in two different ways: for lead-bronze coins, we produced and measured artificial reference samples; for billon coins we simulated different coins with the program XMI-MSIM^[16]. The correction factors obtained were applied to the measured data of the coins. XMI-MSIM was also used to estimate measurement uncertainties resulting from geometrical effects (like embossment).

By these simulations it is underpinned that the uncertainties resulting from patina or surface effects are consistent with the statistical uncertainty obtained from multiple measurements. In contrast to the use of references samples, simulations with XMI-MSIM are more versatile. Finally, some actual results from the measurement of the different coins are discussed.

1.3. Principles, Possibilities and Limitations of X-Ray Fluorescence spectrometry

With X-rays, electrons can be ejected from an atom. This leads to an atom with empty electronic states. The remaining shell electrons cascade downwards to reach the empty states. During this process, characteristic X-ray fluorescence radiation is emitted. This cascade can be seen in figure 2. Because the electric field of every chemical element is different, the X-ray fluorescence radiation exhibits energies that are characteristic for each chemical element, making it identifiable and quantifiable^[17]. The intensities of these characteristic X-rays can be used to calculate the elemental composition of the sample under consideration^[18]. However, for an accurate quantitative measurement both the attenuation of the incoming and outgoing radiation within the sample itself must be considered. Especially, fluorescence (outgoing) radiation might be absorbed again by another atom and thus cause secondary fluorescence, while at the same time the intensity of the primary radiation decreases. This results in a loss of accuracy for the measurement. Figure 3 depicts a typical X-ray fluorescence spectrum obtained from a coin of the Claudius era. The coins of the Claudius and Nero era that were investigated are billon coins, an alloy containing the main elements Cu and Ag. Visible in the spectrum are the K-Lines of Cu and Ag which are the most dominant. Furthermore K- and L-lines of other elements e.g. Au, Sn, Zn and Fe are also visible.

In general, XRF-spectrometry is an easy and fast method to investigate samples. A measurement time of only a few minutes already delivers meaningful results. This allows for a larger number of samples to be investigated with multiple measurements on each object thereby yielding a large set of statistical information. This means an increase in data precision. The obtained data enables, for instance, the classification of samples into distinct groups as well as the recognition of overarching trends among them.

1.4. Measurement of coins with portable XRF

Coins are generally suitable objects for XRF because they are made of characteristic metals or alloys. Elements with an atomic number lower than 11 (sodium, Na), which cannot easily be detected by XRF, are generally no main elements in coins. Although coins are a good example for a sample group containing many similar objects that can be compared on a statistical basis, XRF-measurements are done more commonly on paintings or papyrus inks. In those cases the analysis is simpler and therefore more accurate, because the above-mentioned self‑attenuation in the sample can be neglected. This is due to the limited thickness of the paint in those objects. In contrast, the measurement of coins might not only be influenced by self-attenuation, but also by the presence of patina, or geometric effects (surface roughness) that must be considered. The penetration range of X-Rays may vary, depending on the X-Ray-source used but usually represents a penetration depth of 0.1 mm up to 1 mm. Therefore XRF-measurement data may not represent the core of a coin, but certainly the penetration depth of the X-Rays will be portrayed accordingly. The core of a coin may differ in its composition form the outer composite layers, but according to Ernst Gölitzer^[19] a correlation between core material and outer layers seems plausible and would make vague assumptions about the overall material possible.

Patina effects on the measurement

Often coins build up a patina. Most materials are not resistant to oxidation or corrosion, thus forming a thin chemically modified surface layer. This patina might in general influence an XRF-measurement as the penetration depth of X‑rays is typically on the scale of several µm (depending on the element mixture of the sample and the exact energy of the X‑rays). In principle, it is possible to correct measurements for patina effects^[20]. But because the patina is mostly made up of oxides and therefore the density of that material is typically lower compared to the bulk material, the absorption of X-rays is lower in the patina than the rest of the coin. Especially when several objects can be compared on a statistical basis, patina effects play only a secondary role. Hence, exact determination of the elemental composition is challenging. A removal of the patina must be considered destructive and should therefore be avoided. However, as we will show below, in practical cases the patina might increase measurement uncertainty, but if several measurements are performed on the same object, these uncertainties can be quantified, and a comparison of objects is still possible. This means that the uncertainties resulting from a patina may be somewhat fixed in a statistical way by a large set of data, while a single data point will still be lacking in precision.

Self-absorption and secondary fluorescence

There are several influences on XRF-measurements. The size (solid angle) and the efficiency of the detector have an influence on the measurement, as well as the attenuation of the incident beam, the probability of photon creation, and the attenuation of the induced fluorescence radiation. As described above, additional X‑ray fluorescence can be induced via secondary absorption inside the sample itself. The characteristic fluorescence of a heavy element can induce characteristic fluorescence of lighter elements in the sample, leading to an overrepresentation in intensity of the lighter elements compared to the heavier elements. Accuracy is negatively affected by secondary fluorescence. All these effects might be corrected collectively, in our works using either reference samples or computational simulation of XRF‑measurements.

Surface irregularities

In addition to patina effects and self-absorption as well as secondary fluorescence, the geometric structure of the sample may influence the result of an analysis. The point is that the attenuation of the X-rays depends on the surface geometry (e.g. the embossment of the coins) of the samples. If the surface of the sample is structured, X-rays must travel through more or less coin material, depending on the incoming angle and outgoing angle of radiation (see figure 4).

Because different elements have different absorption coefficients and the penetration depth is also dependent on the energy the elemental X-rays have, the intensity of the X‑ray can differ and lead to an additional uncertainty of the elemental composition. Although this behavior is difficult to treat in a mathematically exact way, we will show that the influence of this effect on the result can be estimated and can be partially overruled by performing several measurements on each sample, improving precision.

2. Experimental and Results

2.1. Coins under investigation

In this work, a total of 43 coins were measured with a portable ELIO SN 1254 XRF‑spectrometer, 20 random lead-bronze coins from the Roman period and 23 billon coins (tetradrachms) issued under Claudius and Nero, respectively. Also, we chose silver coins for the second part of the paper, because silver coins from the early years of Claudius and Nero, between the reintroduction of silver coinage by Tiberius and the Neronian reform, have been underrepresented in literature so far. The main components of the lead-bronze coins are Cu, Sn and Pb; the main components of the billon coins are Cu and Ag. All coins stem from the coin collection of the Department of Classics of the University of Cologne and are listed in table 1 according to their inventory numbers.

2.2. Artificial reference samples

To derive correction factors for lead-bronze coins experimentally (see section 3.1.1 below), we produced 42 samples with known ratios (wt%) of Cu, Sn and Pb (see table 2). The ratios of the metals were selected such that they cover typical compositions of lead-bronze coins.

The amount of Cu varied from 70 to 95 wt%, reflecting the range of historical lead-bronze. The remaining wt% of the sample is split between Sn and Pb also in varying amounts. The powdered pure metals were weighed, mixed in their powdered form and melted for 3 hours without mechanical mixing at 1050 °C in graphite crucibles. This was done to ensure a homogenous melt to produce a coin-like form. It was verified by weighing that material loss due to evaporation was negligible. All in all, 42 different samples were produced. Figure 5 below shows 4 of these reference samples. 

2.3. XRF measurements

To obtain a set of data for each coin that was measured, ten different measurements were done on each coin side. 8 measurements were taken along the rim of the coins and 2 measurements in the center. Measuring spots can be seen in figure 6.

The measurements of coins and reference samples were done with the ELIO device, and the composite analysis was done by the ELIO software. To obtain a more precise data set, only the expected or probable elements of these coins were investigated (i.e., selected as possible components in the analysis software). These were Cu, Ag, Pb and Sn as main components as well as Zn, Fe and Au as secondary components. The reference samples were measured in the same manner as the billon and lead-bronze coins.

3. Results and Discussion

3.1. Correcting measurement data based on reference samples

As described above, to correct the X-ray intensities of the different elements for self-attenuation and secondary fluorescence in coins (or general in thicker samples), correction factors are needed. Such factors can either be developed experimentally or from simulations. In this work both methods were used as described in the next paragraphs.

3.1.1. Correction factors (experimental)

A correction factor for the measurement of Pb/Cu in lead-bronzes was derived experimentally. This was done to enhance accuracy of XRF. The 42 reference samples (section 2.2.) were measured with XRF to deduce the impact of the different metals to each other. The measured mass fractions of Cu, Sn, and Pb of all 42 samples were plotted vs. the actual mass fractions (see figure 7). The measured fractions were taken from output of the ELIO software, averaged over 20 measurements as described above, to increase the precision of the data. The actual mass fractions were calculated from the weightings of the raw materials, see section 2.2. The dashed lines represent linear fits. While the tin mass fractions are very near to their nominal values, the lead and copper values deviate. The Pb concentration is obviously underestimated, and the Cu concentration is overestimated. This agrees with the assumption that secondary absorption plays an important role, because the fluorescence radiation of heavier elements might be absorbed again by lighter elements. Also, the deviation is linear within the given concentration range.

Therefore, a correction factor for the wt% value of lead can be calculated as the reciprocal slope of the linear fit shown in figure 6. This yields the following correction factor.

(1)    = 1.84 ± 0.43